My band is a 3 piece and we've got a new drummer. The bassist and I go way back but lately there's been some tension. I don't feel like the bassist listens to any suggestions I make.

I've been sort of withdrawn from the band however I want to suggest things to practice that make us good instead of decent. Also the other two talk and joke around a lot, they seem to enjoy talking smack about whoever.

Should I just chill and take things slowly? How should I go about engaging myself into this band? How do I address the talking issue without seeming rude/boring?

You'll have to be a little more specific about the suggestions you are making that the bassist is not listening to. Are they song choice suggestions or are they suggested improvements to his playing?

Acting withdrawn isn't going to improve anything. I think you've just got to try and have some fun with your band. It seems that with the addition of the new drummer your band dynamic has changed. You can't change things back to how they were, so you must find new ways to get the most out of band practices. With regards your "things to practice that make us good instead of decent", how you go about it really depends on what the "things to practice" are. You really have to be a little more specific.